A) \[\frac{\sqrt{5}{{\mu }_{0}}I}{2R}\]
B) \[\frac{3{{\mu }_{0}}I}{2R}\]
C) \[\frac{{{\mu }_{0}}I}{2R}\]
D) \[\frac{{{\mu }_{0}}I}{R}\]
Correct Answer: A
Solution :
| [a] The magnetic field at the centre of circular current carrying coil of radius R and current |
| \[I,B=\frac{{{\mu }_{0}}I}{2R}\] |
| Similarly, if current \[=2I,\] then |
| Magnetic field \[=\frac{{{\mu }_{0}}2I}{2R}=2B\] |
| So, resultant magnetic field |
| \[=\sqrt{{{B}^{2}}+{{(2B)}^{2}}}=\sqrt{5{{B}^{2}}}=\sqrt{5}B\] |
| \[=\frac{{{\mu }_{0}}I\sqrt{5}}{2R}\] |
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